Discussion of the relationship between the aerosol extinction coefficient error and background noise
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This paper discusses the relationships among the aerosol extinction coefficient error (AECE), background noise, and distance associated with lidar measurements. The AECE calculation is explained in detail, revealing that the AECE is the product of background noise, range squared, and a relation function. The result of an AECE calculation that uses lidar measurements obtained in Nanjing, China, agrees with a calculation that uses a simulated lidar signal. The AECE equation is verified with lidar measurement data and a simulated lidar signal, indicating the AECE equation is reasonable.
Aerosols are a source of uncertainty and an important cause of climate change. Aerosols also strongly pollute the atmospheric environment and are harmful to public health [1–3]. Consequently, scientists continue to consider aerosol research an important topic, as different aerosol optical properties cause different atmospheric radiation effects, and a database of aerosol optical properties has yet to be established in atmospheric research. High-accuracy aerosol optical properties are necessary for atmospheric studies. For instance, the aerosol extinction coefficient, and the related visibility and optical depth, are essential in meteorology research . Lidar can measure aerosols with high efficiency and range resolution. However, deficiencies still exist in lidar aerosol measurements. Aerosol measurement uncertainty exists for two reasons: the inversion method for the aerosol parameter, which has many assumptions , and systematic error due to the lidar system. Systematic error due to background noise is especially important, because it persists in aerosol lidar measurements. It remains an open question as to how background noise should be handled. Researchers commonly reduce background noise, experimentally, by making lidar measurements at night, using a narrow bandpass filter, and by decreasing the telescope’s field of view. However, few studies have examined aerosol measurement error due to background noise . This paper presents the theoretical calculation of the aerosol extinction coefficient error (AECE) due to background noise. The equation relating the AECE and background noise is calculated in detail. The AECE is calculated using experimental data and a simulated lidar signal.
2 Theory of the AECE
We discuss the relationships among T(r, x), T 0(r, x), F(r, x) with reference to experimental and simulation data, as described below. The calculation results show that F(r, x) is negligibly small.
3 Analysis of aerosol lidar measurement data
The extinction coefficient profile 1 (profile 3) in Fig. 6d is calculated from the simulated signal with constant (without) background noise. Profile 4 in Fig. 6d is the error of the extinction coefficient. The extinction coefficient, profile 2 in Fig. 6d, is the sum of profiles 3 and 4. Recall that profile 1 is the extinction coefficient calculated using (1), and profile 2 is the extinction coefficient calculated from the full AECE theory. Figure 6 shows a small difference between profiles 1 and 2.
In aerosol lidar measurements, the measurement accuracy is of great importance. The accuracy of aerosol optical property depends on several factors, including the boundary value and parameter assumptions, and background noise. According to lidar theory, the relationship between the AECE and background noise, and distance can be calculated. The AECE is proportional to the square of distance r 2, the relation function T(r, x), and the amount of background noise. Here, the relationship between the AECE and background noise has been verified by using aerosol lidar measurements and simulated lidar signals.
This work was supported by the Nature Science Foundation of China under Project 41175033/D0503 and Chinese Public Welfare Industry Special Project GYHY 201006047-5.
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